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Trust, influence, and convergence of behavior in social networks

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  • Pan, Zhengzheng

Abstract

I propose a social learning framework where agents repeatedly take the weighted average of all agents' current opinions in forming their own for the next period. They also update the influence weights that they place on each other. It is proven that both opinions and the influence weights are convergent. In the steady state, opinions reach consensus and influence weights are distributed evenly. Convergence occurs with an extended model as well, which indicates the tremendous influential power possessed by a minority group. Computer simulations of the updating processes provide supportive evidence.

Suggested Citation

  • Pan, Zhengzheng, 2010. "Trust, influence, and convergence of behavior in social networks," Mathematical Social Sciences, Elsevier, vol. 60(1), pages 69-78, July.
  • Handle: RePEc:eee:matsoc:v:60:y:2010:i:1:p:69-78
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    References listed on IDEAS

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    1. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
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    3. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 93-125.
    4. Banerjee, Abhijit & Fudenberg, Drew, 2004. "Word-of-mouth learning," Games and Economic Behavior, Elsevier, vol. 46(1), pages 1-22, January.
    5. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-643, August.
    6. Durieu, Jacques & Solal, Philippe, 2003. "Adaptive play with spatial sampling," Games and Economic Behavior, Elsevier, vol. 43(2), pages 189-195, May.
    7. Shiller, Robert J, 1995. "Conversation, Information, and Herd Behavior," American Economic Review, American Economic Association, vol. 85(2), pages 181-185, May.
    8. Lorenz, Jan, 2005. "A stabilization theorem for dynamics of continuous opinions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 217-223.
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    Cited by:

    1. Grabisch, Michel & Rusinowska, Agnieszka, 2013. "A model of influence based on aggregation functions," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 316-330.
    2. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, pages 240-257.
    3. Diamantaras, Dimitrios & Gilles, Robert P., 2011. "Ambiguity, social opinion and the use of common property resources," Journal of Economic Behavior & Organization, Elsevier, vol. 80(1), pages 210-222.
    4. Zhengzheng Pan, 2012. "Opinions and Networks: How Do They Effect Each Other," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 157-171, February.

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